Ta có:1000000=2⁶.5⁶

Số 1000000 có số ước  là:(6+1).(6+1)=49(ước)

Vậy số 1000000 có 49 ước.

Bài 1:

a) \(a=2\cdot3\cdot5\cdot43\)

\(b=7200=2^5\cdot3^2\cdot5^2\)

\(c-4680=2^3\cdot3^2\cdot5\cdot13\)

b) \(\dfrac{8440}{5910}=\dfrac{8440:10}{5910:10}=\dfrac{844}{591}\)

\(\dfrac{1245}{3450}=\dfrac{1245:15}{3450:15}=\dfrac{83}{230}\)

Bài 2:

a) Ước nguyên tố của 140 là:

\(ƯNT\left(140\right)=\left\{2;5;7\right\}\)

Ước nguyên tố của 138 là:
\(ƯNT\left(138\right)=\left\{3;23;2\right\}\)

b) \(A=\dfrac{2^{10}+4^6}{8^4}\)

\(A=\dfrac{2^{10}+2^{12}}{2^{12}}\)

\(A=\dfrac{2^{10}\cdot\left(1+2^2\right)}{2^{12}}\)

\(A=\dfrac{1+4}{2^2}\)

\(A=\dfrac{5}{4}\)

\(B=\dfrac{6^{10}+15\cdot2^{10}\cdot3^9}{12\cdot8^3\cdot27^3}\)

\(B=\dfrac{2^{10}\cdot3^{10}+5\cdot2^{10}\cdot3^{10}}{2^{11}\cdot3^{10}}\)

\(B=\dfrac{2^{10}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{10}}\)

\(B=\dfrac{1+5}{2}\)

\(B=3\)

2⁶.5⁶

1 000 000 = 2⁶.5⁶

Cách 1:

1 000 000 = 2.500 000 = 2.2.250 000 = 2.2.2.125 000 = 2.2.2.2.62500

= 2.2.2.2.2.31250 = 2.2.2.2.2.2.15625 = 26.5.3125 = 26.5.5.625

= 26.5.5.5.125 = 26.5.5.5.5.25 = 26.5.5.5.5.5.5 = 26.56

Cách 2: 1 000 000 = 106 = (2.5)6 = 26.56

1000000 = 2⁶ x 5⁶  nha   trần thị thu                   ^_^

Ta có:

1000000

=10⁶

=(2.5)⁶

=2⁶.5⁶

Vậy 1000000 phân tích ra thừa số nguyên tố dc 2⁶.5⁶

a: \(35\cdot20+125:5^2\)

\(=700+\dfrac{125}{25}\)

=700+5

=705

\(=3\cdot5\cdot47\)

b: \(5^2\cdot8-\dfrac{60}{2^2}\)

\(=25\cdot8-\dfrac{600}{4}\)

=200-15

=185

\(=5\cdot37\)

c: \(\dfrac{4500}{15}+3^2\cdot10\)

\(=\dfrac{45}{15}\cdot100+9\cdot10\)

=300+90

=390

\(=2\cdot3\cdot5\cdot13\)

d: \(2724-\left(2^3\cdot3^2-2^4\cdot3\right)\)

\(=2724-8\cdot9+16\cdot3\)

\(=2724+48-72=2700\)

\(=3^3\cdot2^2\cdot5^2\)

\(a,=80+13^2:13^2=80+1=81=3^4\\ b,=25\cdot4-2^5:2^4=100-2=98=2\cdot7^2\\ c,=111+16^2:16^2=111+1=112=2^4\cdot7\\ d,=175-\left(75-45\right)=175-30=145=5\cdot29\)

a )

20.4 + 169 : 13²

= 80+169 : 169

=80 + 1

=81

=3⁴

b)5² . 4 -32 :3⁴ 

= 25 . 4 - 32 : 81

= 100 - \(\dfrac{32}{81}\)

= \(\dfrac{8068}{81}\)

a: \(160-\left(2^3\cdot5^2-6\cdot25\right)\)

\(=160-\left(8\cdot25-150\right)\)

=160-(200-150)

=160-50

=110

\(=2\cdot5\cdot11\)

b: \(4\cdot5^2-32:2^4=4\cdot25-32:16=100-2=98=2\cdot7^2\)

c: \(5871:\left\lbrack928-\left(247-82\cdot5\right)\right\rbrack\)

\(=5871:\left\lbrack928-\left(247-410\right)\right\rbrack\)

=5871:[928-247+410]

=5871:1091

d: \(777:7+1331:11^3=111+1=112=2^4\cdot7\)

e: \(6^2:4\cdot3+2\cdot5^2=36:4\cdot3+2\cdot25\)

=27+50

=77

\(=7\cdot11\)

g: \(5\cdot4^2-18:3^2=5\cdot16-18:9=80-2=78=2\cdot3\cdot13\)

h: \(80-\left(4\cdot5^2-3\cdot2^3\right)=80-\left(4\cdot25-3\cdot8\right)\)

=80-(100-24)

=80-76

=4

=2^2

i: \(23\cdot75+25\cdot23+180\)

\(=23\left(75+25\right)+180\)

=2300+180

=2480

\(=2^4\cdot5\cdot31\)

k: \(2^4\cdot5-\left\lbrack131-\left(13-4\right)^2\right\rbrack\)

\(=16\cdot5-\left\lbrack131-81\right\rbrack\)

=80-50

=30

=2*3*5

m: 100:{250:[450-\(\left(4\cdot5^3-2^2\cdot25\right)\) ]}

=100:{250:[450-\(\left(4\cdot125-4\cdot25\right)\) ]}

=100:{250:[450-500+100]}

=100:{250:50}

=100:5

=20

=2^2*5

27= \(3^3\)

a)
27=3³
30=2.3.5
80=2⁴.5
20=2².5
120=2³.3.5